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Suppose we have a signal from a current transformer over a pair of transmission lines. In order to prevent the voltage between the terminations of either of the transmission lines and ground from floating, we need to ground at least one of them somewhere. If we just directly ground one transmission line and then measure voltage between ground and the ungrounded side, will there be negative implications for measurement of common mode noise on both transmission lines? Is it more desirable to, e.g. reference both lines to ground through equal resistance resistors (of course they cannot both be shorted)?

I feel that the answer is no but I'm trying to build a "precise" instrument and I've never studied how to analyze noise in transmission lines, so I'm not confident.

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If we just directly ground one transmission line and then measure voltage between ground and the ungrounded side, will there be negative implications for measurement of common mode noise on both transmission lines?

Yes there will. Consider this example circuit: -

enter image description here

The "sensor" might as well be a current transformer output and, if you have some length of balanced cable between it and your single-ended measurement circuit, then noise or interference won't be seen equally on both inputs of your single-ended amplifier. This is because the input impedances of the single-ended amplifier won't be equal. The "balanced" solution is to do this: -

enter image description here

Because both inputs into the differential receiving amplifier have the same impedance to local ground, the interference waveform is seen equally at both input nodes and, the effect of the differential amplifier is to cancel those signals out. This is a balanced input impedance.

Pictures from this longer answer.

Also, don't forget that your CT may require a burden resistor.

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    \$\begingroup\$ For future reference: I've asked here how to make this work using a differential analog multiplexer before the signal amplifier. \$\endgroup\$ Dec 22, 2020 at 16:06

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